Multi-resolution Shape Analysis via Non-Euclidean Wavelets: Applications to Mesh Segmentation and Surface Alignment...

Area of Science:

• Computer Vision
• Computer Graphics
• Medical Imaging
• Harmonic Analysis

Background:

• 3-D shape mesh analysis requires multi-resolution understanding of local and global topology.
• Traditional Wavelets are not applicable to non-uniformly sampled data like general graphs.
• A need exists for methods that provide consistent analysis across multiple scales for complex shapes.

Purpose of the Study:

• To adapt harmonic analysis results for Non-Euclidean Wavelets applicable to 3-D shape analysis.
• To develop algorithms for shape analysis problems in computer vision and medical imaging.
• To demonstrate the utility of Non-Euclidean Wavelets for multi-resolution shape characterization.

Main Methods:

• Derived Non-Euclidean Wavelets from recent harmonic analysis results.
• Developed dual-domain descriptors for characterizing local/global topology.
• Adapted the framework for key point extraction, 3-D shape segmentation, and landmark-free surface alignment.

Main Results:

• Non-Euclidean Wavelets provide native multi-resolution behavior for shape topology.
• A simple and competitive 3-D shape segmentation algorithm was developed.
• A novel method for landmark-free surface alignment was achieved, with a uniqueness theorem derived.

Conclusions:

• Non-Euclidean Wavelets offer a powerful framework for diverse 3-D shape analysis tasks.
• The developed algorithms show state-of-the-art performance in segmentation and alignment.
• This approach extends Wavelet analysis to non-uniform data, broadening its applicability.